Raising the bar

A good definition follows the sequence: motivation -> definition proper -> discussion/application.

They say: Figure 2.2 is a special type of bar graph called a Pareto chart . Named after Italian economist Vilfredo Pareto (1848–1923) who advocated its use, it is a bar graph with categories ordered by their frequency, from the tallest bar to the shortest bar. The Pareto chart is often used in business applications to identify the most common outcomes, such as identifying products with the highest sales or identifying the most common types of complaints that a customer service center receives. The chart helps to portray the Pareto principle, which states that a small subset of categories often contains most of the observations. For example, Figure 2.2 shows that three categories (coal, nuclear, and natural gas) were responsible for about 88% of U.S. electricity sources. (Agresti and Franklin, p.31)

I say: Imagine that you are taking an AP Stats exam and you have to give the definition of the Pareto chart based on the above description. What would you say? I think the problem here is that the right sequencing is violated. Besides, a new definition better sinks in if it is related to something students already know. Here is my definition:  the Pareto chart is the same as a histogram, except that the observations are put in the order of decreasing frequencies.